Should the contestant keep Door #1 or switch to Door #2?

Question A

..A game show gives a contestant a choice of 3

doors. Behind one of the doors is a Ferrari.

Behind the other 2 doors are garbage cans.

..The contestant picks Door #1. Monty (the host)

asks, “Are you sure you want to stick with Door

#1? Let me help you out.�Monty then opens

Door #3 to reveal a garbage can.

..Should the contestant keep Door #1 or switch to

Door #2? Explain.

Question B

Suppose that A and B are events with P(A) = 0.4 and P(B) = 0.2. Find P(A
. B) if

(a) A and B are mutually exclusive events.

(b) A and B are independent events.

(c) P(B | A) = 0.25

(d) B is a subset of A; that is, all the outcomes contained in B are
also contained in A.

Question C

5% of a population has a certain genetic condition. A test for this
condition correctly detects it with probability 0.99. However, the test
indicates the condition is present in 15% of cases where it is actually

absent. Suppose a randomly select individual from the population is
tested. Fine the probability that

(a) the individual has the genetic condition (G) and the test says they
have it (T).

(b) the individual does not have the condition and the test still says
they have it.

(b) the test indicates the condition is present.

(c) the individual has the condition given that the test says they have
it.